Random-anisotropy effects in the second-order phase transition of the 2D Blume-Capel model

Quan D. Nguyen; Son N. Bui; H. Phong Nguyen; H. Giang Bach

doi:10.15625/0868-3166/21614

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Authors

Quan D. Nguyen Faculty of Physics, University of Science, Vietnam National University, 334 Nguyen Trai Street, Thanh Xuan, Hanoi, Vietnam https://orcid.org/0009-0000-5317-8441
Son N. Bui Faculty of Physics, University of Science, Vietnam National University, 334 Nguyen Trai Street, Thanh Xuan, Hanoi, Vietnam https://orcid.org/0009-0002-4210-6674
Phong H. Nguyen Faculty of Physics, University of Science, Vietnam National University, 334 Nguyen Trai Street, Thanh Xuan, Hanoi, Vietnam https://orcid.org/0000-0001-6080-7090
Bach H. Giang Faculty of Physics, University of Science, Vietnam National University, 334 Nguyen Trai Street, Thanh Xuan, Hanoi, Vietnam https://orcid.org/0000-0002-1516-1363

DOI:

https://doi.org/10.15625/0868-3166/21614

Keywords:

Blume-Capel model, random anisotropy, effective field theory, differential operator, second-order phase transition

Abstract

We report on the second-order phase transition of two-dimensional (2D) magnetic materials under the influence of random anisotropy in the context of the Blume-Capel model employing an effective field theory and the differential operator method. By analyzing the temperature dependence of magnetization, we thoroughly explore the second-order ferromagnetic-to-paramagnetic (FM-PM) phase transition at the critical temperature $T_C$. When the magnitude of the random anisotropy $D$ and its probability $p$ is sufficiently large, the magnetization equation becomes divergent and unsolvable at a critical temperature, indicating the emergence of a tricritical point and a first-order phase transition. Additionally, we produce a phase diagram for the second-order phase transition presenting the relation between the critical temperature and anisotropy amplitude at various probabilities.

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References

O. Amhoud, N. Zaim, M. Kerouad and A. Zaim, Monte Carlo study of magnetocaloric properties and hysteresis behavior of the double perovskite Sr₂CrIrO₆, Phys. Lett. A 384 (2020) 126443.

G. D. Ngantso, Y. E. Amraoui, A. Benyoussef and A. E. Kenz, Effective field study of Ising model on a double perovskite structure, J. Magn. Magn. Mater. 423 (2017) 337.

O. E. Rhazouani, A. Benyoussef and A. E. Kenz, Phase diagram of the double perovskite Sr₂CrReO₆: Effective-field theory, J. Magn. Magn. Mater. 377 (2015) 319.

O. K. T. Nguyen, P. H. Nguyen, N. T. Nguyen, C. T. Bach, H. D. Nguyen and G. H. Bach, Monte Carlo investigation for an Ising model with competitive magnetic interactions in the dominant ferromagnetic-interaction regime, Commun. Phys. 33 (2023) 205.

I. Lawrie and S. Sarbach, Phase Transitions and Critical Phenomena, vol. 9. Academic Press, 1984.

A. Maritan, M. Cieplak, M. R. Swift, F. Toigo and J. R. Banavar, Random-anisotropy Blume-Emery-Griffiths model, AIP Conf. Proc. 286 (1992) 231.

C. Buzano, A. Maritan and A. Pelizzola, A cluster variation approach to the random-anisotropy Blume-Emery-Griffiths model, J. Phys.: Condens. Matter 6 (1994) 327.

M. Blume, Theory of the first-order magnetic phase change in UO₂, Phys. Rev. 141 (1966) 517.

H. Capel, On the possibility of first-order phase transitions in Ising systems of triplet ions with zero-field splitting, Physica 32 (1966) 966.

H. Capel, On the possibility of first-order transitions in Ising systems of triplet ions with zero-field splitting II, Physica 33 (1967) 295.

H. Capel, On the possibility of first-order transitions in Ising systems of triplet ions with zero-field splitting III, Physica 37 (1967) 423.

A. Benyoussef, T. Biaz, M. Saber and M. Touzani, The spin-1 Ising model with a random crystal field: the mean-field solution, J. Phys. C: Solid State Phys. 20 (1987) 5349.

E. Albayrak, The spin-1 Blume-Capel model with random crystal field on the Bethe lattice, Phys. A 390 (2011) 1529.

D. Lara and J. Plascak, General spin Ising model with diluted and random crystal field in the pair approximation, Phys. A 260 (1998) 443.

A. Benyoussef and H. Ez-Zahraouy, Magnetic properties of a transverse spin-1 Ising model with random crystal-field interactions, J. Phys.: Condens. Matter 6 (1994) 3411.

I. Puha and H. Diep, Random-bond and random-anisotropy effects in the phase diagram of the Blume-Capel model, J. Magn. Magn. Mater. 224 (2001) 85.

N. S. Branco and B. M. Boechat, Real-space renormalization-group study of the two-dimensional Blume-Capel model with a random crystal field, Phys. Rev. B 56 (1997) 11673.

E. Bezerra, M. G. da Silva and J. R. de Sousa, First-order transition of the spin-1 Blume-Capel model with random anisotropy using effective-field theory, Phys. A 615 (2023) 128510.

S. Yan and L. Deng, Thermodynamic properties of bond dilution Blume-Capel model with random crystal field, Phys. A 308 (2002) 301.

C. E. I. Carneiro, V. B. Henriques and S. R. Salinas, Mean-field phase diagram of the spin-1 Ising ferromagnet in a Gaussian random crystal field, J. Phys. A: Math. Gen. 23 (1990) 3383.

H. B. Callen, A Note on Green Functions and the Ising Model, Phys. Lett. 4 (1963) 161.

R. Honmura and T. Kaneyoshi, Contribution to the new type of effective-field theory of the Ising model, J. Phys. C: Solid State Phys. 12 (1979) 3979.

J. Tucker, Generalized Van der Waerden identities, J. Phys. A: Math. Gen. 27 (1994) 659.

T. Kaneyoshi, Phase diagrams of a spin-one Ising model with a random crystal field in the correlated effective-field treatment, Phys. Status Solidi B 170 (1992) 313.

L. Onsager, Crystal statistics. I. A two-dimensional model with an order-disorder transition, Phys. Rev. 65 (1944) 117.

A. Siqueira and I. Fittipaldi, New effective-field theory for the Blume-Capel model, Phys. A 138 (1986) 592.